A221130 -id:A221130 - cp's OEIS frontend

A199116 a(n) = 6*4^n + 1.

7, 25, 97, 385, 1537, 6145, 24577, 98305, 393217, 1572865, 6291457, 25165825, 100663297, 402653185, 1610612737, 6442450945, 25769803777, 103079215105, 412316860417, 1649267441665, 6597069766657, 26388279066625, 105553116266497, 422212465065985, 1688849860263937

Offset: 0

Vincenzo Librandi, Nov 04 2011

Bisection (odd part) of A181565 and A201630. - Bruno Berselli, Dec 04 2011

First differences of A221130, a(n) = A221130(n+2) - A221130(n+1). - Jaroslav Krizek, Jan 02 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).

Cf. A140529, A181565, A201630, A221130.

Magma
```
[6*4^n+1: n in [0..30]];
```

6*4^Range[0,30]+1 (* or *) LinearRecurrence[{5,-4},{7,25},30] (* Harvey P. Dale, Apr 18 2024 *)

a(n) = 4*a(n-1) - 3.
a(n) = 5*a(n-1) - 4*a(n-2).
G.f.: (7-10*x)/((1-x)*(1-4*x)). - Bruno Berselli, Nov 04 2011
From Elmo R. Oliveira, May 08 2025: (Start)
E.g.f.: exp(x)*(6*exp(3*x) + 1).
a(n) = A140529(n) + 2. (End)

A221129 Numbers of form k*2^n + n where 1 <= k < 2^n and n > 0.

Original entry on oeis.org

3, 6, 10, 11, 14, 19, 20, 27, 35, 36, 37, 43, 51, 52, 59, 68, 69, 70, 84, 100, 101, 116, 132, 133, 134, 135, 148, 164, 165, 180, 196, 197, 198, 212, 228, 229, 244, 261, 262, 263, 264, 293, 325, 326, 357, 389, 390, 391, 421, 453, 454, 485, 517, 518, 519, 520, 521

Offset: 1

Jaroslav Krizek, Jan 02 2013

nonn

Subsequence of primes: 3, 11, 19, 37, 43, 59, 101, 197, 229, 263, ...

			a(6) = 19 = 2 *2^3 + 3.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A221130, A199116.

N:= 1000: # to get all terms <= N
sort([seq(seq(k*2^n+n,k=1..min(2^n-1,(N-n)/2^n)),n=1..ilog2(N))]); # Robert Israel, Jan 21 2019

seqUpTo[n_] := Select[Union@Flatten@Table[k*2^h + h, {h, Floor@Log[2, n]}, {k, Min[2^h - 1, Floor[n/2^h]]}], # <= n &]; seqUpTo[521] (* Giovanni Resta, Jan 08 2013 *)

cp's OEIS Frontend

A199116 a(n) = 6*4^n + 1.

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